Rovellifest 1

Carlo Rovelli has recently put 3 papers on the arXiv, which have attracted some attention within the blogsphere (see here, here, here and here). The one that concerns us here at QQ is the paper about EPR in the relational approach to QM. I don't want to comment on the particular argument in that paper, which seems fine as far as it goes, but I do want to say a couple of things about Rovelli's approach in general, since it seems to be a popular topic at the moment. The main ideas of the approach can be found in Rovelli's original paper.

Here is an (admittedly cartoonish) summary:

1. We should shift attention from things like the measurement problem and instead try to derive QM from the idea that it is a theory of the information about one system that is available relative to other systems.

2. Quantum states are not absolute concepts and the state of a system is only defined relative to some other reference systems. Different reference systems do not have to agree on this state. If they do come to agreement it is only after the reference systems themselves interact with each other according to some Hamiltonian.

3. The question of whether a system has some particular property has no absolute meaning. However, some property of a system can be well-defined relative to some other system, provided the systems happen to have interacted in such a way that the second system records the appropriate information about the first system.

4. All the relational states just represent the subjective point of view that one system has about another. There is no absolute meaning to such states and no meaningful "wave-vector of the universe" can be constructed because there is no external system for it to enter into relations with.

5. This is all just a twist on the usual kind of relationalism that we have in other physical theories, e.g. special and general relativity.

In my opinion, there is a good deal wrong with relational QM as formulated by Rovelli, although I am not particularly opposed to relationalism in general. In this post, I'll make some comments about 4 and 5. A forthcoming "Rovellifest 2" post will point out a problem with 3, which I believe is more serious.

To address 5, it is worth noting a striking disanalogy between relational QM and other sorts of relational theories in physics. For example, in Newtonian mechanics we are very used to the idea that that there is no absolute meaning of the position of a particle A, but you can define its distance to a reference system B. This is generally different from the distance of A relative to another reference system C. Similarly, there is no absolute notion of when two events are simultaneous in special relativity, but this is well defined relative to any inertial reference frame.

However, in these cases it is always possible to find some transformation that relates the descriptions relative to different reference frames, provided you know the relations between the frames themselves, e.g. the Lorentz transformations in special relativity.

Now consider a quantum system composed of a subsystem A and two observers B and C. Suppose both B and C separately interact with A, possibly measuring different observables on A. Relative to B, A is supposed to have some definite property after this interaction and similarly for C. However, you generally can't convert between B and C's description of the situation if you only know the state of B relative to C. You can if they happened to measure the same observable, but that's a very special case.

In fact, the only way to relaibly convert between different observers relative states of the same system is to know the entire "wave-vector of the universe", something that is meaningless for Rovelli due to 4.

So, it seems we are left with two options:

1. Add in a "state of the universe" so that one can reliably transform between different descriptions of the same subsystem.

2. Abandon the classical notion that one can reliably transform between different descriptions of the same system.

Adopting 1 would essentially entail accepting an Everettian/many-worlds type scenario, something that Rovelli is keen to distance himself from. Therefore, I conclude that he must accept 2.

Abandoning reliable transformations is not a completely absurd thing to do, but it is important to note that this is a departure from what we usually mean by the term "relational". I am still not entirely convinced that it is consistent, although I haven't managed to think up a scenario where it would cause a problem yet. My suspicion is that it might be attacked by a "Wigner's Enemy" type of argument of the sort that was levelled against Chris Fuchs' Bayesian approach by Amit Hagar, which seems much more relevant to the relational approach than to its original target.

N.B. "Wigner's Enemy" is a new name I just thought up for the argument. I figure he must be an enemy rather than a friend because friends don't usually try to erase your memory.

10 Comments on “Rovellifest 1”

Well you are starting to scratch an itch that has been bothering me; especially with that ‘state of the universe’ thingy.

Are we expected to accept that making one single measurement defines the state throughout all space-time? I hope not, this is just determenism in sheeps clothing.

So the battle rages thus: Perhaps wave functions are only defined on single light cone slices through space-time. Different measurements can intersect along two dimensional surfaces, but this is okay because measure theory only requires that the states be defined almost everywhere, which means we can leave wave functions undefined at the intersection of light cones. However this means that we can only every make a countably infinite number of observations of the universe, not a continum of observations.

I’m not inclined to take problems to do with the wavefunction too seriously. I trust the empirical predictions of QM, encapsulated in the probability rule, but don’t attach too much meaning to any particular way of writing down the formalism. We could use the Heisenberg picture, or any of the various Wigner-type distributions instead of wavefunctions and generate identical predictions. Each of these gives a different intuition abour what reality should be like.

I think there is a formalism out there, waiting to be discovered, that makes much more sense in a relativistic context than any way QM has been written down before. Discovering such a thing could be the key to understanding QM for the universe as a whole. That’s just my opinion though, and I am happy to let the quantum gravity experts worry about these problems until I can come up with a better idea.

The thing that we tend to forget about Schordinger’s Cat is that we can always do an autopsy on the cat to get a rough idea of when it died.

I’d like to forward a motion to remove the word ‘observation’ from all interpretations of QM and replace it with the word ‘interaction’. This would make QM processes a bit more similar to Markov processes.

Do the yeas have it? Motion carried?

With regard to quant-ph/0506228 because Lorentz boosts don’t perserve volume elements (go ahead take that determinant, make my day) I would be cautious of relativistic theories that do not include changes in the normalization and orthoganality of QM states. There is a trick to get around this, but my lips are sealed out of fear of being called a crack pot, cracked pot, or just a general crack smoker.

More generally, there is a perfectly good retrodictive formalism for QM wherein states evolve backwards from measurement events instead of forwards from preparations. That’s the formalism you use to infer when the cat died. However, the retrodictive state is in general very different from the predictive state. You get into a problem if you regard the predictive state as a complete description of reality and ignore the retrodictive state. The same is true in classical probability of course, which is just more evidence that we should be skeptical of the reality of any sort of quantum state.

Replacing “observation” with “interaction” is at the heart of what Rovelli and also the Everettian’s are trying to do. The problem is that we are forced to adopt a very odd ontology in both these attempts.

For me, the main issue is the “reality problem”. If we deny reality both to quantum states and to the usual notion of hidden variables then only the probability rule is left to connect the quantum formalism to things that really happen in the universe. It would be nice to think that science can describe what is really going on in the world in the absence of measuring devices, observers, etc., but I don’t think any interpretation of QM gives a compelling answer to this yet.

I said that Lorentz boosts don’t perserve volume elements, what was I thinking about?!! Of course they do. Perhaps I was thinking about line elements? Now tranlational invariance of state normalization is not gauraneted in curved space-times like the Schwardchild metric, or other solutions where the speed of light varies on a cosmic scale.

Perhaps what I was thinking about was the Dirac solution for the electron. The inner product of wave four vectors will is not invariant with respect to Lorentz boosts. So two states that are orthongonal in one reference frame may not be in a moving reference frame.